Real Algebraic and Analytic Geometry
Submission: 2004, February 11.
In this article we show that the set of Dirichlet-regular boundary points of a bounded domain of dimension up to 4, definable in an arbitrary $o$-minimal structure on the field IR, is definable in the same structure. Moreover we give estimates for the dimension of the set of non-regular boundary points, recognizing wether the structure is polynomially bounded or not. This paper extends the results from the author's thesis, where the problem was solved for polynomially bounded $o$-minimal structures expanding the real field.
Mathematics Subject Classification (2000): 03C64, 31B15, 35J25.
Keywords and Phrases: Dirichlet-regularity, $o$-minimal structures.
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